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## Homework Statement

L = - [itex]\Sigma[/itex]

_{x,y}(P(x,y) log P(x,y)) + [tex]\lambda[/tex] [itex]\Sigma[/itex]

_{y}(P(x,y) - q(x))

This is the Lagrangian. I need to maximize the first term in the sum with respect to P(x,y), subject to the constraint in the second term.

The first term is a sum over all possible values of x,y.

The second term is a sum over all possible values of ONLY y.

## Homework Equations

Given above.

## The Attempt at a Solution

I know I have to differentiate L with respect to P(x',y') where x',y' are fixed values.

The idea is that the first term consists of a sum of P(x,y) over all possible x,y. So, we just need to differentiate L with respect to P(x',y') while keeping all other P(x,y) constant.

But how do I differentiate the second term with respect to P(x',y')? It is a sum over all possible y values.

I know the solution is supposed to be [tex]\lambda[/tex] when the second term is differentiated with respect to a particular P(x',y') but how do we obtain that?

THANKS! :)

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